线性代数 · free preview

Vectors

1. Systems of Linear Equations: Geometry

Systems of Linear Equations: Geometry

2. Introduction

Introduction

3. Vectors in $\mathbb{R}^n$

Vectors in $\mathbb{R}^n$

4. Vector Algebra and Geometry

Vector Algebra and Geometry

5. Linear Combinations

Linear Combinations

6. What a vector is

Which statement about vectors is true?

7. Vector arithmetic

Let $v=\begin{pmatrix}1\\2\end{pmatrix}$ and $w=\begin{pmatrix}-1\\3\end{pmatrix}$ . Which of the following is $2v - w$ ?

8. Vocabulary: scalars

In one word: the real number used to stretch or shrink a vector, as in $cv$ , is called a ______ .

9. Combining vectors

Let $u = \begin{pmatrix}1\\0\\-2\end{pmatrix}$ and $v = \begin{pmatrix}-1\\1\\1\end{pmatrix}$ . Compute $2u - 3v$ and enter the three coordinates separated by commas (for example: 1,2,3).

10. A zero combination

Find weights $x_1,x_2,x_3$ with $x_1 = 1$ such that $x_1w_1 + x_2w_2 + x_3w_3 = 0$ , where

w_1 = \begin{pmatrix}1\\2\\3\end{pmatrix},\qquad w_2 = \begin{pmatrix}4\\5\\6\end{pmatrix},\qquad w_3 = \begin{pmatrix}7\\8\\9\end{pmatrix}.

Enter $x_1,x_2,x_3$ separated by commas (for example: 1,2,3).

11. In your own words

In your own words, state the single most important definition or theorem of this section, and explain what it says.

Practice this interactively

Free account · instant grading · spaced review that schedules itself.

Start this course — free